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Outline

Title
Abstract
Key Takeaways
Introduction
The Basic Questions We Address
Basics of the Statistical Mechanics of Flocking
Data Collection Techniques
Exact Results
The Role of Leadership in Consensus Finding
Summary and Conclusions
References
FAQs

Collective Motion

Profile image of Tamás VicsekTamás VicsekProfile image of Anna LazarAnna Lazar
https://doi.org/10.1016/J.PHYSREP.2012.03.004
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70 pages

Abstract

Wereview the observations and the basic laws describing the essential aspects of collective motion — being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, so that readers with a variety of background could get both the basics and a broader, more detailed picture of the field. The observations we report on include systems consisting of units ranging from macromolecules through metallic rods and robots to groups of animals and people. Some emphasis is put on models that are simple and realistic enough to reproduce the numerous related observations and are useful for developing concepts for a better understanding of the complexity of systems consisting of many simultaneously moving entities. As such, these models allow the establishing of a few fundamental principles of flocking. In particular, it is demonstrated, that in spite of considerable differences, a number of deep analogies exist between equilibrium statistical physics systems and those made of self-propelled (in most cases living) units. In both cases only a few well defined macroscopic/collective states occur and the transitions between

Key takeaways
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  1. Collective motion exhibits universal patterns across diverse systems, including living organisms and non-living entities.
  2. Simple models, like the Vicsek Model, reveal critical behavior and phase transitions in collective motion.
  3. The concept of leadership in flocks can emerge from differences in information among individuals, affecting decision-making.
  4. Adhesive interactions among cells influence tissue movement and sorting, highlighting the role of cohesion in collective behavior.
  5. Hydrodynamic interactions play a crucial role in the collective dynamics of self-propelled particles, affecting their motion patterns.

Related papers

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Patterns, transitions and the role of leaders in the collective dynamics of a simple robotic flock
Máté Nagy

Journal of Statistical Mechanics-theory and Experiment, 2011

We have developed an experimental setup of very simple self-propelled robots to observe collective motion emerging as a result of inelastic collisions only. A circular pool and commercial RC boats were the basis of our first setup, where we demonstrated that jamming, clustering, disordered and ordered motion are all present in such a simple experiment and showed that the noise level has a fundamental role in the generation of collective dynamics. Critical noise ranges and the transition characteristics between the different collective patterns were also examined. In our second experiment we used a real-time tracking system and a few steerable model boats to introduce intelligent leaders into the flock. We demonstrated that even a very small portion of guiding members can determine group direction and enhance ordering through inelastic collisions. We also showed that noise can facilitate and speed up ordering with leaders. Our work was extended with an agent-based simulation model, too, and close similarity between real and simulation results was observed. The simulation results show clear statistical evidence of three states and negative correlation between density and ordered motion due to the onset of jamming. Our experiments confirm the different theoretical studies and simulation results in the literature on the subject of collision-based, noise-dependent and leader-driven self-propelled particle systems.

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Collective motion with anticipation: Flocking, spinning, and swarming
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Physical Review E, 2015

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Application of statistical mechanics to collective motion in biology
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Physica A: Statistical Mechanics and its Applications, 1999

Our goal is to describe the collective motion of organisms in the presence of uctuations. Therefore, we discuss biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In our models the particles corresponding to organisms locally interact with their neighbours according to simple rules depending on the particular situation considered. Numerical simulations indicate the existence of new types of transitions. Depending on the control parameters both disordered and long-range ordered phases can be observed. In particular, we demonstrate that (i) there is a transition from disordered to ordered motion at a ÿnite noise level even in one dimension and (ii) particles segregate into lanes or jam into a crystalline structure in a model of pedestrians.

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Flocking dynamics with voter-like interactions
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We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a two-dimensional space at a constant speed in a direction that is randomly assigned initially. Then, at every step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle. We investigate the time evolution of the global alignment of particles measured by the order parameter ϕ, until complete order ϕ = 1.0 is reached (polar consensus). We find that ϕ increases as t 1/2 for short times and approaches exponentially fast to 1.0 for long times. Also, the mean time to consensus τ varies nonmonotonically with the density of particles ρ, reaching a minimum at some intermediate density ρ min. At ρ min , the mean consensus time scales with the system size N as τ min ∼ N 0.765 , and thus the consensus is faster than in the case of all-to-all interactions (large ρ) where τ = 2N. We show that the fast consensus, also observed at intermediate and high densities, is a consequence of the segregation of the system into clusters of equally-oriented particles which breaks the balance of transitions between directional states in well mixed systems.

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Macroscopic models of collective motion and self-organization
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Séminaire Laurent Schwartz — EDP et applications, 2012

In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view of its possible extensions to other kinds of collective motion.

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We implement a self-organized flocking behavior in a group of mobile robots and analyze its transition from an aligned state to an unaligned state. We briefly describe the robot and the simulator platform together with the observed flocking dynamics. By experimenting with robotic and numerical systems, we find that an aligned-to-unaligned phase transition can be observed in both physical and simulated robots as the noise level is increased, and that this transition depends on the characteristics of the heading sensors. We extend the Vectorial Network Model to approximate the robot dynamics and show that it displays an equivalent phase transition. By computing analytically the critical noise value and numerically the steady state solutions of this model, we show that the model matches well the results obtained using detailed physics-based simulations.

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Scale-Free Correlations in Flocking Systems with Position-Based Interactions
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Journal of Statistical Physics, 2014

We consider a model of self-propelled agents with spring-like interactions that depend only on relative positions, and not on relative orientations. We observe that groups of these agents self-organize to achieve collective motion (CM) through a mechanism based on the cascading of self-propulsion energy towards lower elastic modes. By computing the correlation functions of the speed and velocity fluctuations for different group sizes, we show that the corresponding correlation lengths are proportional to the linear size of the group and have no intrinsic length scale. We argue that such scale-free correlations are a natural consequence of the position-based interactions and associated CM dynamics. We hypothesize that this effect, acting in the context of more complex realistic interactions, could be at the origin of the scale-free correlations measured experimentally in flocks of starlings, instead of the previously argued proximity to a critical regime.

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The Study of Results Simulation of Collective Motion
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International Journal of Computer Applications, 2012

The collective behavior/motion has always been one of the most fascinating phenomena since men started to observe nature which remains a real natural phenomenon, were it is typical in our social environment. The study of collective behavior on a large scale also enables us to better understand different approaches to study in the small scale. In this study, we discuss the principal effect of the control parameters: The binder cumulant, density and the size of system with three zones repulsion, orientation and attraction on the collective motion in the 2D. Furthermore a simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in system of particles. In our simulation, the particles equivalent to agents interact with their neighbors by choosing at each time step a velocity depending on their direction. The aim of this article is to extend the model proposed earlier by Viscek et al. Numerical simulations showed that depending on the control parameters both disordered and long-range ordered phases can be observed and the corresponding phase space domains are separated by singular critical lines.

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Collective behavior of interacting self-propelled particles
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Physica A: Statistical Mechanics and its Applications, 2000

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References (336)

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  2. 8. Leadership in groups of mammals and crowds ........................................................................................................................ 98
  3. 3.9. Lessons from the observations...................................................................................................................................................
  4. Basic models ............................................................................................................................................................................................
  5. 1. Simplest self-propelled particle (SPP) models ..........................................................................................................................
  6. 1.1. The order of the phase transition ...............................................................................................................................
  7. 1.2. Finite size scaling .........................................................................................................................................................
  8. 2. Variants of the original SPP model ............................................................................................................................................
  9. 2.1. Models without explicit alignment rule ....................................................................................................................
  10. 2.2. Models with alignment rule........................................................................................................................................
  11. 3. Continuous media and mean-field approaches ........................................................................................................................
  12. 4. Exact results ................................................................................................................................................................................
  13. 4.1. The Cucker-Smale model............................................................................................................................................
  14. 4.2. Network and control theoretical aspects ...................................................................................................................
  15. 5. Relation to collective robotics....................................................................................................................................................
  16. Modeling actual systems ........................................................................................................................................................................ 5.1. Systems involving physical and chemical interactions ............................................................................................................
  17. 1.1. The effects of the medium...........................................................................................................................................
  18. 1.2. The role of adhesion ....................................................................................................................................................
  19. Swarming bacteria.......................................................................................................................................................
  20. 2. Models with segregating units...................................................................................................................................................
  21. 3. Models inspired by animal behavioral patterns ....................................................................................................................... 5.3.1. Insects...........................................................................................................................................................................
  22. 3.2. Moving in three dimensions -fish and birds............................................................................................................
  23. 4. The role of leadership in consensus finding..............................................................................................................................
  24. 5. Relationship between observations and models ......................................................................................................................
  25. Summary and conclusions...................................................................................................................................................................... Acknowledgments .................................................................................................................................................................................. References................................................................................................................................................................................................
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What explains the observed transition from disordered to ordered states in flocking systems?add

The study shows that increasing interaction strength among units leads to a continuous phase transition from disorder to order, with critical exponents characterizing the process.

How does self-propulsion differ between biological and non-biological systems?add

Self-propelled biological units, like fish, exhibit non-conservation of momentum during interactions, unlike traditional physical systems where momentum conservation applies.

When did giant number fluctuations become significant in collective motion research?add

Giant number fluctuations were first reported in a 2004 study of shaken rods, revealing unique scaling laws in non-equilibrium systems.

What factors influence leadership emergence in animal collective motion?add

Leadership emerges from differences in information among group members; higher levels of informed individuals generally lead to better decision-making accuracy.

How can the principles of collective motion apply to robotics?add

The principles of collective motion are used to develop algorithms for controlling robot swarms, enabling efficient, coordinated behaviors based on local interactions.

About the authors
Tamás Vicsek
Eötvös Loránd University Budapest, Faculty Member
Anna Lazar

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